Multiplicity bounds and the subrepresentation theorem for real spherical spaces

DOI10.1090/S0002-9947-2014-06427-1zbMath1334.22016arXiv1309.0930OpenAlexW2963596544MaRDI QIDQ2787988

Bernhard Krötz, Henrik Schlichtkrull

Publication date: 7 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.0930

zbMATH Keywords

orbithomogeneous spaceHarish-Chandra modulesubrepresentation theoremdistribution vector

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46)

Related Items (15)

Volume growth, temperedness and integrability of matrix coefficients on a real spherical space ⋮ Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture ⋮ Representations of reductive groups distinguished by symmetric subgroups ⋮ Classification of reductive real spherical pairs. I: The simple case ⋮ Bounds on multiplicities of spherical spaces over finite fields ⋮ The infinitesimal characters of discrete series for real spherical spaces ⋮ Harmonic analysis for real spherical spaces ⋮ Geometric counting on wavefront real spherical spaces ⋮ Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms ⋮ Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs ⋮ Classification of reductive real spherical pairs. II: The semisimple case ⋮ Classification of spherical algebraic subalgebras of real simple Lie algebras of rank 1 ⋮ Annihilator varieties of distinguished modules of reductive Lie algebras ⋮ Simple compactifications and polar decomposition of homogeneous real spherical spaces ⋮ GENERALIZED ZETA INTEGRALS ON CERTAIN REAL PREHOMOGENEOUS VECTOR SPACES

Cites Work

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• Finite orbit decomposition of real flag manifolds
• Decay of matrix coefficients on reductive homogeneous spaces of spherical type
• Characters, asymptotic and n-homology of Harish-Chandra modules
• Asymptotic behavior of matrix coefficients of admissible representations
• Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula
• Finite multiplicity theorems for induction and restriction
• The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
• The local structure theorem for real spherical varieties
• Lie groups beyond an introduction

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